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Work Sampling Study Size Calculator

Work out work sampling study size instantly with clear inputs, formula shown and shareable results.

About Work Sampling Study Size Calculator

Work sampling estimates a proportion, so sample size follows the binomial formula n = z^2 x p x (1-p) / e^2, where e is the absolute accuracy in proportion points. Studies of rare activities need far more observations, because the required sample rises steeply as p falls for a fixed relative accuracy.

Formulas

Work sampling size

n = z^2 x p x (1 - p) / e^2

Duration

Study days = observations required / observations per day

Worked example

With the default values below, Work Sampling Study Size Calculator returns Observations Required of 801. Change any input above and every figure here is recalculated in your browser.

Inputs used

Expected Proportion Of Activityaccepts 0.1–99.9 %
25 %
Desired Absolute Accuracyaccepts 0.01–50 % points
3 % points
Confidence Levelone of 90%, 95%, 99%
95%
Observations Per Dayminimum 1
60

Results

Observations Required
801
Study Duration
13.34
Z Value Used
1.960
Relative Accuracy
12.00%

Step by step

  1. 1Values used
  2. 2Work sampling size
  3. 3Duration
  4. 4Observations Required= 801
  5. 5Study Duration= 13.34
  6. 6Z Value Used= 1.960
  7. 7Relative Accuracy= 12.00

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why must observations be random?

Any regular pattern lets operators anticipate the observer and lets cyclical work bias the result. Draw observation times from a random schedule each day.

How do I pick the initial p?

Use a pilot study of 100-200 observations, or the most pessimistic plausible value. Using p = 0.5 gives the largest and therefore safest sample size.

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